Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
- Lasarzik, Robert
2010 Mathematics Subject Classification
- 35Q35 35D99 76D05
- Weak-strong uniqueness, phase transition, Navier--Stokes, Cahn--Hilliard, existence, thermodynamical consistent, dissipative solutions, relative energy
In this paper, existence of generalized solutions to a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model introduced in  is proven in any space dimension. The generalized solvability concepts are measure-valued and dissipative solutions. The measure-valued formulation incorporates an entropy inequality and an energy inequality instead of an energy balance in a nowadays standard way, the Gradient flow of the internal variable is fulfilled in a weak and the momentum balance in a measure-valued sense. In the dissipative formulation, the distributional relations of the momentum balance and the energy as well as entropy inequality are replaced by a relative energy inequality. Additionally, we prove the weak-strong uniqueness of the proposed solution concepts and that all generalized solutions with additional regularity are indeed strong solutions.
- Nonlinear Analysis, 213 (2021), pp. 112526/1--112526/33, DOI 10.1016/j.na.2021.112526 .